LK uses \(k\) -opt ([1]} [1]}) as the optimization method to find optimal or sub-optimal solutions, and escapes from the local optimal solution by initializing new routes. A 3-opt move is shown in Figure REF . At each iteration, the 3-opt attempts to improve the tour by cutting three edges \(x_1, x_2, x_3\)  in the current tour and replacing with three new edges \(y_1, y_2, y_3\) .
Obviously, the key point of \(k\) -opt is how to select these \(x_i\)  and \(y_i\) , \(i\in {1, ..., k}\) , i.e. the edges to be removed and the edges to be added.
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